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  "body": "\n## Summary\n\nThe wave equation $u_{tt} = c^2 \\Delta u$ is the basic [[hyperbolic partial differential equation|92C3S03AQZ]].\nIt describes vibrating strings and membranes, sound, and light in vacuum.\nIts solutions travel at the finite speed $c$.\nIn one space dimension every solution is a sum of a wave moving left and a wave moving right.\nIt is the model for the theory of hyperbolic equations, just as the [[heat equation|VP2HN86VAG]] is for parabolic ones.\n\n## Explanations\n\n### L1 human\n\nPluck a guitar string: the displacement $u(x, t)$ of the string obeys the wave equation.\nThe acceleration $u_{tt}$ of a piece of string is proportional to its curvature $u_{xx}$, because tension pulls a bent piece back toward straight.\nA bump on the string splits into two bumps that move apart at speed $c$ without changing shape.\nFor example, $u(x, t) = \\sin(x - ct)$ is a wave that moves to the right at speed $c$.\n",
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